Abstract
This article proposes a generalized threshold latent variable model for flexible threshold modeling of time series. The proposed model encompasses several existing models, and allows a discrete valued threshold variable. Sufficient conditions for stationarity and ergodicity are investigated. The minimum description length principle is applied to formulate a criterion function for parameter estimation and model selection. A computationally efficient procedure for optimizing the criterion function is developed based on a genetic algorithm. Consistency and weak convergence of the parameter estimates are established. Moreover, simulation studies and an application for initial public offering data are presented to illustrate the proposed methodology.
Highlights
The threshold autoregressive (TAR) model, proposed by [58], has enormous popularity in a wide range of applications
One important direction is on generalized linear models with thresholds, such as the generalized threshold mixed model (GTMM) ([53]) and the generalized threshold stochastic regression model (GTSRM) ([54])
Threshold modeling has been extended to heteroscedasticity of time series, for example, the double-threshold autoregressive moving average conditional heteroskedastic (DTARMACH) model ([38]), the threshold stochastic volatility (THSV) model ([56]), the multiple-threshold double autoregressive (MTDAR) model ([33]), and the threshold double autoregressive model (TDAR) ([34])
Summary
The threshold autoregressive (TAR) model, proposed by [58], has enormous popularity in a wide range of applications. It allows the modeling of diverse behaviors under different regimes, which provides flexible descriptions of many real-world scenarios. Conditions for strict stationarity and ergodicity are investigated only for the self-excited threshold autoregressive (SETAR) model ([11]), the TAR model with order p ([3]), the DTARMACH model in [38], the HAR model in [36], the MTDAR model in [33], and the TDAR model in [34].
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